The Number of Interlacing Equalities Resulting from Removal of a Vertex from a Tree
Name
Farber-2015-Number of interlacing.pdf
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323.4 KB
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Author(s)
Farber, Miriam
Johnson, Charles
Zhang, Leon
Date Issued
July 2015
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Farber, Miriam, Charles Johnson, and Leon Zhang. “The Number of Interlacing Equalities Resulting from Removal of a Vertex from a Tree.” SIAM Journal on Discrete Mathematics 29, no. 3 (January 2015): 1245–1258. © 2015, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We consider the set of Hermitian matrices corresponding to a given graph, that is, Hermitian matrices whose nonzero entries correspond to the edges of the graph. When a particular vertex is removed from a graph a number of eigenvalues of the resulting principal submatrix may coincide with eigenvalues of the original Hermitian matrix. Here, we count the maximum number of “interlacing equalities” when the graph is a tree and the original matrix has distinct eigenvalues. We provide an upper bound and lower bound for the count and discuss some conditions under which the count is equal to the upper bound.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/130931692
